We are currently using an early version of the Oracle Data Access Components (10.2.0.4g client) on our Windows 7 machines. I would like to also use the latest ODAC (11.2.0.3.20). Is it possible for these to be installed side by side on the same machine and for the .NET code to reference the appropriate client for its use? Are there other considerations that I should take in to account?

Yes, you can do that. You may need to remove the Oracle.DataAccess Policy file from the GAC though if the 10.2 app uses 2.x framework..
http://www.oracle.com/technetwork/database/windows/faq-093106.html#policy

The only other common "gotcha" that folks frequently hit is that adding a new home doesn't make it use the tnsnames.ora file from the other home, so you'll need to configure it in the new home as well, or set TNS_ADMIN environment variable to the location you want the .ora files to get picked up from.

It's likely you'll only be able to get one version of Oracle Developer Tools for Visual Studio working on a single machine (the Visual Studio addin that enables Server Explorer and things like Entity Designer). This should not be an issue except in a few edge cases. Let me know if you run into issues with this.